Learn by example
understanding
prediction
communication
You are doing this all the time - there are many reasons to make this process explicit (computer aided modeling)
Inputs: Varying; think x of a x vs y regression
Parameters: single values that influence relationships in the model
Transfer Function (model): Equations that transfer inputs to outputs given parameters
Outputs: what you want to estimate
What are the processes/relationships that you think are important to translate inputs to output
Transfer function (mathematical representation)
Parameters, values that influences how the model relationships work
There are often multiple “boxes” internal to a model
Often more complicated than a simple regression…
So we need to think through what the relationships are; the processes are that we want to take in to account
Conceptual models are a good place to start
Precipitation = Evapotranspiration + Change in Storage
P = ET + ΔS
(at global scales ΔS includes streamflow since that water is still “stored” in the earth
Goal - estimate streamflow fromm multiple source (surface and subsurface)
More complex model couple sub-models
How do ecological and human factors interact to influence fire regimes
There are many different ways to classify models
A useful classification looks at how models deal with space, time, and process
Useful because the type of model will have implications for how you build and use/run the model
Stochastic: Model output is the probability of flood events of a magnitude greater than 500 m3/sec given rainfall probability distribution (artificial or generated from data) for a 100km2 watershed Deterministic: Model output is the depth of flood given a rainfall event of 10cm over a 100km2 watershed
Lumped - single point in space, or space doesn’t matter
Spatially distributed - model is applied to different “patches” in space spatial units are independent
spatial units interact with each other
Static - Processes or Variables modeled do not evolve with time
Dynamic - model elements evolve through time - and variables/results at one time step typically depends on previous time step
Abstract - relationship between inputs and output depends on parameters that don’t necessarily have a physical meaning
Physically based - parameters do have a physical meaning (could be measured) - relationships derived from first principles (theory) of how things work
serc.carlton.edu Abstract
Physically based
Abstract Physically based http://ks.water.usgs.gov/pubs/reports/paclim99.html
Pictorial representation of how you think about your system, and what needs to be included in the model to answer your questions (or achieve your modelling goal)
There are many software tools available for generating conceptual models, I like
[Diagrams.net]{https://www.diagrams.net/}
Some model designers uses standard symbols for the different model components
Building Models
Conceptual Models
Impact of smoke from fires on health of agricultural workers What is ’smoke” What is “health” What is an “agricultural worker”. …leads to your conceptual model
What are your inputs-outputs
What’s in the box (the model itself) that gives you a relationship between outputs and inputs
Transfer function
Parameters, values that influences how the model relationships work
Conceptual………….Mathematical
Stochastic………….Deterministic
Lumped………….Spatially Distributed: SPACE
Static………….Dynamic : TIME
Abstract………….Physically/Process Based
but biggest differences may often be the degree specific processes/parameters are accounted for
Input: Reservoir height (height) and flow rate (flow)
Output: Instantaneous power generation (W/s)
Parameter: Reservoir Efficiency (K)
Conceptual model
Input: Reservoir height and flow rate
Output: Instantaneous power generation (W/s)
Parameters: K Efficiency , ρ (density of water), g (acceleration due to gravity)
P = ρ * h * r * g * K Efficiency;
P is Power in watts, ρ is the density of water (~1000 kg/m3), h is height in meters, r is flow rate in cubic meters per second, g is acceleration due to gravity of 9.8 m/s2, K Efficiency is a coefficient of efficiency ranging from 0 to 1.
This is a static (one point in time), deterministic, lumped (one place) model; its more or less physically based
If we expand the model to compute power production over a year, where inputs were streamflow into the reservoir - Dynamic Model
If we expand to model power production from all the reservoirs in California, accounting for spatial patterns of snowmelt inputs and upstream-downstream relationships - Spatially Distributed Model
If we modified the model to estimate the probability distribution of power production, given a probability distribution of reservoir levels - Stochastic Model
With your conceptual model from Tuesday’s class -
Clearly define your goal (question you want to answer, hypothesis you want to test, prediction you want to make) - as precisely as possible
Develop a conceptual model - draw it!
Design or Select your model
Implement the model
Evaluate the model and quantify uncertainty
Apply the model to the goal
Communicate model results
Design conceptual model
Translate conceptual model into a mathematical representation
Choose programming language
Define inputs (data type, units)
Define output (data type, units)
Define model structure
Write model
Document the model (meta data)
Test model
For this assignment you will work in pairs
Your goal is to develop a conceptual model of almond yield - the goal will be able to predict how almond yields might change if seasonal precipitation or air temperature patterns change in California - we’d like to know mean, minimum and average yield anomolies given a climate prediction
The Lobell et al. 2006 paper will be the source for your model; specifically look at the equations in table 2.
Draw a conceptual model to represent your model that will translate inputs to output, with parameters that shape the relationship between inputs an outputs - on your diagram list what your inputs, parameters and outputs are with units
Write a simple R function that implements your conceptual model
Run your model for the clim.txt data that is posted on Canvas
We will build on this on Tuesday’s class
Grading Rubric
Conceptual model (30 pts)
R Implementation (30 pts)
Extra Credit - a diagram that that works for all tree yields (20 pts)